continuous

/kənˈtɪnjʊəs/

adjective

1.

prolonged without interruption; unceasing: a continuous noise

2.

in an unbroken series or pattern

3.

(maths) (of a function or curve) changing gradually in value as the variable changes in value. A function f is continuous if at every value a of the independent variable the difference between f(x) and f(a) approaches zero as x approaches aCompare discontinuous (sense 2) See also limit (sense 5)

4.

(statistics) (of a variable) having a continuum of possible values so that its distribution requires integration rather than summation to determine its cumulative probability Compare discrete (sense 3)

Relating to a line or curve that extends without a break or irregularity.

A function in which changes, however small, to any x-value result in small changes to the corresponding y-value, without sudden jumps. Technically, a function is continuous at the point c if it meets the following condition: for any positive number ε, however small, there exists a positive number δ such that for all x within the distance δ from c, the value of f(x) will be within the distance ε from f(c). Polynomials, exponential functions, and trigonometric functions are examples of continuous functions.